# Differential Geometry/notation help

1. Apr 18, 2012

### EV33

1. The problem statement, all variables and given/known data

I have this theorem which I am having trouble understanding due to notation.

Theorem: Define S,S'$\subseteq$ℝ3 to be surfaces. Let f:S→S' be a smooth map. f is a local isometry if for all p in S, and all w1,w2 in TpS,
<w1,w2>=<dfp(w1),dfp(w2)>.

The thing I don't get, is what does dfp(w1) mean?
What action is going on between dfp and w1?

$df_p$ is the derived mapping from the tangent space at p in S to the tangent space at f(p) in S'.